Problem: Express this product in scientific notation: $(6.80\times 10^{2})\times (4.00\times 10^{-4})$
Solution: Start by collecting like terms together. $= (6.80\times 4.00) \times (10^{2}\times 10^{-4})$ When multiplying exponents with the same base, add the powers together. $= 27.2 \times 10^{2\,+\,-4}$ $= 27.2 \times 10^{-2}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the left without changing the value of our answer. $ $ We can use the fact that $27.2$ is the same as $2.720 \times 10$ $ = {2.720 \times 10} \times 10^{-2} $ $= 2.720\times 10^{-1}$